The value 1 in Box [3,1] must lie in Row 8.The value 4 in Box [1,1] must lie in Column 1.The value 5 in Box [3,3] must lie in Row 9.The value 7 in Box [1,1] must lie in Column 1.The value 8 in Box [2,2] must lie in Row 6.The values 1, 4 and 8 occupy the cells (4,5), (6,5) and (6,6) in some order.The cell (7,5) is the only candidate for the value 7 in Column 5.

I think it's safe to ignore the first four observations for immediate purposes. Once we've restricted the position of the 8 in Box 5, we observe that the value 7 can't occupy the cell r4c5, which leaves just a single candidate position in Column 5.

The first four observations help to solve the remainder of the puzzle - which should be very straightforward from here.

The value 1 in Box [3,1] must lie in Row 8.The value 4 in Box [1,1] must lie in Column 1.The value 5 in Box [3,3] must lie in Row 9.The value 7 in Box [1,1] must lie in Column 1.The value 8 in Box [2,2] must lie in Row 6.The values 1, 4 and 8 occupy the cells (4,5), (6,5) and (6,6) in some order.The cell (7,5) is the only candidate for the value 7 in Column 5.

I think it's safe to ignore the first four observations for immediate purposes. Once we've restricted the position of the 8 in Box 5, we observe that the value 7 can't occupy the cell r4c5, which leaves just a single candidate position in Column 5.

Thanks for that - I had already considered the first four points, so it all fell into place very quickly after that.

Just looking at box 5 again, I have the minimum pencilmarks as follows:(4,4) = 3 7(4,5) = 1 4 7(5,4) = 3 7 9(5,7) = 3 9(6,5) = 1 4 8(6,6) = 3 4 8and am trying to work out the general rule to describe how we know that "The values 1, 4 and 8 occupy the cells (4,5), (6,5) and (6,6) in some order" to make sure I don't miss this sort of thing again...

It's a little easier (to me at least), to note that 3,7 & 9 are the only candidates for (4,4), (5,4) & (5,7) - thus eliminating these digits from the other cells...

So, the general rule is "when N cells have only N candidates between them, those N candidates may be eliminated from the other cells in the unit". N is 3 in this case. This is what's come to be known as Milo's rule 2.

The value 1 in Box [3,1] must lie in Row 8.The value 4 in Box [1,1] must lie in Column 1.The value 5 in Box [3,3] must lie in Row 9.The value 7 in Box [1,1] must lie in Column 1.The value 8 in Box [2,2] must lie in Row 6.The values 1, 4 and 8 occupy the cells (4,5), (6,5) and (6,6) in some order.The cell (7,5) is the only candidate for the value 7 in Column 5.

I'm fairly new to this, although having some success, but am confused by the above.

Why must the value 1 in Box [3,1] lie in Row 8? There is also a candidate in row 9.Why must the value 4 in Box [1,1] lie in Column 1? There are also two candidates in row 2.

The value 1 in Box [3,1] must lie in Row 8.The value 4 in Box [1,1] must lie in Column 1.The value 5 in Box [3,3] must lie in Row 9.The value 7 in Box [1,1] must lie in Column 1.The value 8 in Box [2,2] must lie in Row 6.The values 1, 4 and 8 occupy the cells (4,5), (6,5) and (6,6) in some order.The cell (7,5) is the only candidate for the value 7 in Column 5.

Why must the value 4 in Box [1,1] lie in Column 1? There are also two candidates in row 2.

I'll start with those two for now - I'm obviously missing something!

I don't have the fully pencilmarked puzzle to hand, but... If you look at where 4 could go in column 1, it should only appear in box 1 (albeit in two cells). This means you can eliminate the possible 4s from column 2 in box 1.

Applying this logic should, if I recall, explain the first five statements in the original post.

The value 1 in Box [3,1] must lie in Row 8.The value 4 in Box [1,1] must lie in Column 1.The value 5 in Box [3,3] must lie in Row 9.The value 7 in Box [1,1] must lie in Column 1.The value 8 in Box [2,2] must lie in Row 6.The values 1, 4 and 8 occupy the cells (4,5), (6,5) and (6,6) in some order.The cell (7,5) is the only candidate for the value 7 in Column 5.

I'm fairly new to this, although having some success, but am confused by the above.

Why must the value 1 in Box [3,1] lie in Row 8? There is also a candidate in row 9.Why must the value 4 in Box [1,1] lie in Column 1? There are also two candidates in row 2.

I'll start with those two for now - I'm obviously missing something!

Thanks in advance,

Chris.

The basics are; that each Box,Row and Column, contain the numbers 1-9.

We see that there is already a 1 in Row 9, cell(9,6) in the original starting grid, this precludes a value of 1 appearing any where else on Row 9.Comparing where the value 1 can be placed in Boxes [3,1][3,3] should help you.

If you want to try to work it out yourself don't look at the grid below, but put in a 1 in col 3, row 4. This was an either / or 1 for that box and I had to take a leap of faith to get it all to work out.